|
|
Subject:
Coke can Volume dimensions
Category: Science > Math Asked by: curius-ga List Price: $2.00 |
Posted:
04 Dec 2005 03:22 PST
Expires: 03 Jan 2006 03:22 PST Question ID: 601197 |
how many pepsi cans fit into cargo space of 36 cu ft? |
|
There is no answer at this time. |
|
Subject:
Re: Coke can Volume dimensions
From: markvmd-ga on 04 Dec 2005 06:55 PST |
Curius-- How about you meet a Researcher partway for that big $2 payment and go measure a Pepsi can? |
Subject:
Re: Coke can Volume dimensions
From: ansel001-ga on 04 Dec 2005 16:04 PST |
The answer could depend to some extent on the shape of the 36 cubic feet. If it is very long and wide but only one inch high, the answer would be zero. Also, are there restrictions on stacking? Can some cans be upright and others sideways? Do they need to be kept in the purchasing packages of twelve or more, or can they be individually put in the cargo bay? |
Subject:
Re: Coke can Volume dimensions
From: manuka-ga on 04 Dec 2005 23:46 PST |
Well, we can at leat get an approximate upper bound fairly quickly. Now the canonical soft-drink can is 375mL, so with an allowance for the can itself I'll call each can 400mL. 36 cu ft is 28.3 L (assuming I've calculated that correctly), so it looks like at most 70 cans or so - using 375mL per can gives us 75 cans max. As other posters have mentioned, a lot depends on the precise shape of the cargo space; for maximal efficiency it could be shaped like a really, really tall cylinder just wide enough to fit a can (or 70-odd cans) inside, and as previously mentioned it might be impossible to get any cans inside. But whatever shape, you won't get any more than 70-75 cans in it. |
Subject:
Re: Coke can Volume dimensions
From: ansel001-ga on 05 Dec 2005 01:40 PST |
Manuka, You have indeed defined the most efficient shape for the 36 cubic feet of space with your really, really tall cylinder. But I think that a liter is less than a cubic foot. I pulled a standard 12 fluid ounce soft drink can out of the fridge (and drank it). The label says it has 354 milliliters in it. I looked up the conversion factor from cubic inches to liters. It is 61.02374 cubic inches per liter. This amounts to 21.60240538 cubic inches per can. There are 1728 cubic inches per cubic foot. Therefore there are 79.99 cans per cubic foot or 2879 cans per 36 cubic feet. Of course even with your maximally efficient shaped space, the cans have a ridge on top and something similar on bottom. So less cans would fit. The above calculation in essence, assumes that we have one big can. Before we pursue it any further, I think Curius should measure his can of Pepsi for us. I must say though, this problem is much more interesting if it is academic rather than practical. Here is a link to Erich's Packing Center http://www.stetson.edu/~efriedma/cirinsqu/ It shows the most efficient packing arrangements for circles in squares. Depending how this problem plays out, this could be relevant in some way. |
Subject:
Re: Coke can Volume dimensions
From: myoarin-ga on 05 Dec 2005 03:26 PST |
I got as far as the Pepsi website and found that the cans are only 8 oz, at least no others were mentioned. |
Subject:
Re: Coke can Volume dimensions
From: ticbol-ga on 05 Dec 2005 05:13 PST |
A lot. More than 12,000 cans. That is based only on about 1/4 inch as the thickness of the flattened pepsi can. So if the cans are to be run over by a real heavy roller compactor, the type they use in road construction, I bet more than 15,000 cans will fit inside your 36-cu.ft. cargo space. Are you in the business of recycling alum cans? |
Subject:
Re: Coke can Volume dimensions
From: rracecarr-ga on 05 Dec 2005 12:07 PST |
Model a coke can as a perfect cylinder with a volume of 12 fl oz = 0.012533 cu. ft. Assume that the cargo space is a rectangular prism that fits tightly around rectantularly stacked cans. Then each can takes up a block of space with a square cross section, and the volume it takes up is greater than the volume of the can by a factor of 4/pi (the ratio of the area of a square to the circle that fits inside it). So the volume taken up by each can is 0.015957 cu. ft., and 2256 of them will fit in your cargo space. Of course, you could fit a few more if you where to stagger rows of cans so that they fit together like a honeycomb, but I'm assuming the cans stay in their plastic 6-pack holder ring-things. If you do 'stagger' the cans, and you have not gotten extremely creative with the shape of your cargo space, there is an upper limit of 2605 cans. This is assuming the cross-sectional area taken up by each can is greater than the actual cross section of the can by a factor of 2*sqrt(3)/pi, which is tightest you can pack circles into a plane. |
Subject:
Re: Coke can Volume dimensions
From: frankcorrao-ga on 05 Dec 2005 13:57 PST |
According to some website, a soda can is 6" high with a 2" diameter. That's ~24"^3. A cubic foot is 1728 cubic inches. That's 72 cans per cubic foot. To make sure it makes sense conceptually, that would be two 6x6 stacks. Sounds about right. So 72x36 is 2592. Initally the > 2000 figures posted by others did not make any conceptual sense to me, so a coworker and I made a back of the envelope check. And after some thinking, the conceptualization is a bit more clear, though 2500 still sounds somewhat high to me. |
Subject:
Re: Coke can Volume dimensions
From: myoarin-ga on 06 Dec 2005 02:38 PST |
Let's see: 36 cubic ft is 1.02 cubic meters or 1020 liters. That divided by 375 ml (or 0.375 ltr) is 2,718.4, the max. number of contents of cans of that size that would go in a TANK of 36 cubic ft. BUT, we are stacking cans so we lose some space. Base area of a can: 3.14159r^2; area of the square it occupies: 4r^2. Thus stacked cans occupy only 0.7854 of the base area each requires (3.14159/4). This reduces the volume of Pepsi in 36 cubic ft to 2,135 cans, and we must subtract something for the space lost from the shape of the ends of the cans and the bit of air space within them. This is getting pretty close to the 2000 can estimates. Personally, I prefer Ticbol's answer. |
Subject:
Re: Coke can Volume dimensions
From: stephanbird-ga on 06 Dec 2005 04:39 PST |
"BUT, we are stacking cans so we lose some space. Base area of a can: 3.14159r^2; area of the square it occupies: 4r^2." Iff you stack in squares, yes, but you can also stack in triangles and hexagons, a bit like honeycomb... S |
Subject:
Re: Coke can Volume dimensions
From: fractl-ga on 06 Dec 2005 12:43 PST |
There are a few different ways to pack cans into a rectangular space. I?m just using the three most common (and most efficient) methods below: Assuming Aligned Cans: __________ |()()()()| |()()()()| / |()()()()| H/ __ /__ (__) | W // / <soda can Assuming staggered Cans: D| (/_/ ___________ __________ | |()()()() | |()()()()| | ()()()()| or | ()()() | |()()()() | |()()()()| w=width, d=depth, h=height (bear in mind that the cans that will fit depend on which side is determined to be ?up?. Laying the cans down in the box will have the same effect as rotating the box). Measurements are in inches, as this is based on a 2?x2?x6? can. In the first case the optimal number of cans would be floor(w/2)*floor(d/2)*floor(h/6). If mod(w,2)>1, the staggered arrangement will have the same number of cans in each row. The maximum number of cans in this case would be floor(w/2)*floor(((1.1547*d)-.3094)/2)*floor(h-6) In the event that mod(w/2)<1 you?d be better of using the aligned can arrangement. If you copy the following formulas into Excel (with ?WIDTH:? on cell A1) this should calculate the number of cans that can fit into the specified box. Just replace the ???s with the dimensions (in inches). ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ WIDTH: ? DEPTH: ? HEIGHT: ? STAGGERED: =FLOOR(A2/2,1)*FLOOR(((1.1547*A4)-0.3094)/2,1)*FLOOR(A6/6,1) ALIGNED: =FLOOR(A2/2,1)*FLOOR(A4/2,1)*FLOOR(A6/6,1) MAX: =MAX(A12,A9) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Sample Solutions: 24?x36?x72? = 2952 cans (using the 72? side as the depth) 36?x36?x48? = 2916 cans (using the 48? side as the depth) 40?x40?x40? = 2640 cans (a cubic box is not optimal) 2?x2?x15552? = 2592 cans (a tower is also not optimal) 102?x101?x6? = 2958 cans (I believe this is the most possible) |
Subject:
Re: Coke can Volume dimensions
From: rracecarr-ga on 06 Dec 2005 15:14 PST |
OK, clearly the biggest problem here is inaccuracy in describing the dimensions of a pepsi can. I don't know if this changes from country to country, but in the US, pepsi cans contain 12 fluid oz of pepsi, which is 355 mL. It says so right on the can. There may be a bit of air space inside the can, and the aluminum itself takes up some room. Also the cans aren't perfect cylinders, but taper in at the ends, and the bottom is indented. So I measured a can of Coke (I would have used a Pepsi can, if the stuff wasn't so vile--I think the dimensions are probably the same.) 2 inches in diameter by 6 inches high is a very inaccurate description. The diameter of my specimen was not very constant (the can is not very round) but the average diameter, within a fraction of a millimeter, is 66 mm, or 2.60 inches. The overall height of the can is 123 mm, or 4.84 inches. However, the effective height is a bit less, say 120 mm (4.72 in) because cans will 'nest' together a bit, with the bottom rim of one fitting inside the top rim of another. Using these dimensions, the volume of the cylinder taken up by a can is 13.9 oz or 411 ml or 25.1 cubic inches. So if you stack them 'six pack' style into a rectilinear 36 cubic foot space, you can fit at most 1947 of them. If you stagger them, the upper limit is 2249. |
Subject:
Re: Coke can Volume dimensions
From: myoarin-ga on 06 Dec 2005 22:25 PST |
Yes, indeed, Rracecarr, that two inch can was misleading, This site suggests that the most usual diameter for drinks cans is 65 mm, probably the size of your can. Of course I agree entirely with your +/- 2000 can solution. :) while being a little pleased that my calculation based on the can volume, regardless of the dimensions, gives this result. Anse1001 should like that too. http://www.geocities.com/and_pollett/beer52.htm Cheers, Myoarin |
Subject:
Re: Coke can Volume dimensions
From: rracecarr-ga on 07 Dec 2005 11:38 PST |
No, my can has a diameter of 66.0 mm. |
Subject:
Re: Coke can Volume dimensions
From: curius-ga on 08 Dec 2005 00:05 PST |
the pepsi can dimensions are H=12 cms / 4.5 in W=6.5 cms / 2.2 in 330 ml in a can |
Subject:
Re: Coke can Volume dimensions
From: manuka-ga on 11 Dec 2005 19:41 PST |
This is country-specific - here in Australia the standard soft-drink can has a 375 mL capacity, which is why I used that figure in my calculation (pity I forgot to multiply the volume by 36 when I was converting to litres). So it looks like our cans are a little bit bigger than yours. |
Subject:
Re: Coke can Volume dimensions
From: fractl-ga on 12 Dec 2005 07:36 PST |
curius, even with the 12cm x 6.5cm can dimension, there are a few more pieces of info one needs before getting an answer. 1. The number of cans that can fit in a 36 cu ft vary dramatically as the dimensions of the space change. What are the exact dimensions in the space you'd like to pack with cans? 2. Can this be considered an abstract calculation or a physical one? By this I mean, could the 'cans' be substituted with 12x6.5 cylinders or should I take the interlocking tops, the flexing of the aluminum, or any other properties of the cans into account? 3. Just for my own curiosity...why do you want to know how many cans fit? -Fractl |
If you feel that you have found inappropriate content, please let us know by emailing us at answers-support@google.com with the question ID listed above. Thank you. |
Search Google Answers for |
Google Home - Answers FAQ - Terms of Service - Privacy Policy |